Scheduling with Machine Cost

Imreh, Csanád; Noga, John

doi:10.1007/978-3-540-48413-4_18

Cited by 27 publications

(14 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In addition to its theoretical significance, one of the motivations for this problem comes from the need to minimize energy consumption in large data centers, such as those used by Google and Amazon (see [12,29] for the practical significance of this problem). This problem has been studied earlier in both the offline [19,29] and online [17,27,28] models. While near-optimal algorithms were known in the offline model, we give the first near-optimal online algorithm for this problem.…”

Section: Unrelated Machine Scheduling With Startupmentioning

confidence: 99%

“…They give offline algorithms for the problem using different techniques. For the online problem with identical machines, [17,28] give O(1)-competitive algorithms where the objective is the sum of the makespan and startup cost. These are extended to the case where machines have speed either 1 or s, with more general startup costs, by Imreh [27].…”

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Online Mixed Packing and Covering

Bhaskar¹,

Fleischer²

2013

Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms

View full text Add to dashboard Cite

Recent work has shown that the classical framework of solving optimization problems by obtaining a fractional solution to a linear program (LP) and rounding it to an integer solution can be extended to the online setting using primal-dual techniques. The success of this new framework for online optimization can be gauged from the fact that it has led to progress in several longstanding open questions. However, to the best of our knowledge, this framework has previously been applied to LPs containing only packing or only covering constraints, or minor variants of these. We extend this framework in a fundamental way by demonstrating that it can be used to solve mixed packing and covering LPs online, where packing constraints are given offline and covering constraints are received online. The objective is to minimize the maximum multiplicative factor by which any packing constraint is violated, while satisfying the covering constraints. Our results represent the first algorithm that obtains a polylogarithmic competitive ratio for solving mixed LPs online.We then consider two canonical examples of mixed LPs: unrelated machine scheduling with startup costs, and capacity constrained facility location. We use ideas generated from our result for mixed packing and covering to obtain polylogarithmic-competitive algorithms for these problems. We also give lower bounds to show that the competitive ratios of our algorithms are nearly tight.

show abstract

Section: Unrelated Machine Scheduling With Startupmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Online Mixed Packing and Covering

Bhaskar¹,

Fleischer²

2013

Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms

View full text Add to dashboard Cite

show abstract

“…The most popular one involves a machine activation cost. Imreh and Noga (1999) considered the problem where the number of machines used is a variable, which can be easily justified by a machine activation cost, opportunity cost or lease cost. Since the problem is defined in an online scheduling context, the algorithm initially does not have any machine at its disposal but at any point in time additional machines may be purchased or leased.…”

Section: Introductionmentioning

confidence: 99%

Bi-criteria scheduling with machine assignment costs

Leung¹,

Lee²,

Pinedo³

2012

International Journal of Production Economics

View full text Add to dashboard Cite

“…* In the scheduling problem of Imreh and Noga [16], one must decide when to buy new machines. Buying machines is expensive, but with more machines, more work can be accomplished per time unit.…”

Section: Introductionmentioning

confidence: 99%

“…The competitive ratio of the scheduling problem F21rj]Cmax is at least 1.3~9~3.The problem of scheduling with machine cost is introduced in[16]. We show the first randomized lower bound for the list variant of this problem: THEOREM 8.3.…”

mentioning

confidence: 97%

A guessing game and randomized online algorithms

Seiden

2000

Proceedings of the Thirty-Second Annual ACM Symposium on Theory of Computing

View full text Add to dashboard Cite

We present the first general framework for proving lower bounds for randomized online algorithms using the von Neumann/Yao principle. This framework encompasses and explains many existent lower bound results, and allows us to prove several new ones. The foremost of the new results is a lower bound of 1.58197 for the online TCP acknowledgment problem of Dooly, Goldman and Scott [11]. Other new results include: a lower bound of 1.34880 for randomized online two-machine flow shop scheduling, a lower bound of 1.15775 for randomized online total completion time scheduling on parallel machines and a lower bound of 1.06532 for scheduling with machine cost. Out method provides a sort of 'Master theorem' for proving randomized lower bounds.

show abstract

Scheduling with Machine Cost

Cited by 27 publications

References 7 publications

Online Mixed Packing and Covering

Online Mixed Packing and Covering

Bi-criteria scheduling with machine assignment costs

A guessing game and randomized online algorithms

Contact Info

Product

Resources

About